NCERT Class XII Chapter
Ray Optics and Optical Instruments
Questions With Solutions

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Question : 1
Total: 38
A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
Solution:  
The object is kept between f and C. So the image should be real, inverted and beyond C. To locate the sharp image, screen should be placed at the position of image

The focal length f =
R
2
= - 18 cm
Object distance u = – 27 cm
Using mirror formula
1
v
+
1
u
=
1
f

or
1
v
+
1
27
=
1
18
or
1
v
= -
1
18
+
1
27

1
v
= -
3+2
54
1
v
= -
1
54

v = – 54 cm
Size of image can be calculated by magnification
m = -
v
y
= -
I
O
or -
I
O
= -
v
u

I
+2.5
= -
54
27
⇒ I = - 5 cm
So, the image is inverted and magnified.
Thus in order to locate the sharp image, the screen should be kept 54 cm in front of concave mirror and image on the screen will be observed real, inverted and magnified. If the candle is moved closer to the mirror, the real image will move away from the mirror, hence screen has to be shifted away from the mirror to locate the sharp image.
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